I think the short story captures this well. Weights (connections) are the essential and philosophically important part. They do the thinking, memory, singing etc.
As you said, it's not in any way intrinsic to the LLM, though it may be a very necessary optimization on today's hardware.
IMO, we are probably talking about a 6x slow down (for typical english). You would need to be absolutely stupid not to implement some kind of optimisation along these lines.
Slower and maybe a little dumber; But it would work.